I'm not sure I understand the question, but jQuery functions such as slideUp() can take a callback method that will be fired after the operation is completed.
You can use the callback to show the next alert.
http://api.jquery.com/slideDown/
For what it's worth, jQuery code (such as in your example) that looks like:
$('#messageDrop').addClass('visible').slideDown().delay('2000').slideUp().removeClass('visible')
...is hard to read and maintain (IMO). Adding callbacks or nested callbacks increases this complexity. Consider declaring a few local variables and working with those objects rather than chaining a bunch of statements together.
Also, the stop() method is your friend when dealing with (potentially conflicting) jQuery animations: http://api.jquery.com/stop/